Module « scipy.stats »

Fonction boxcox - module scipy.stats

Signature de la fonction boxcox

def boxcox(x, lmbda=None, alpha=None, optimizer=None) 

Description

boxcox.__doc__

Return a dataset transformed by a Box-Cox power transformation.

    Parameters
    ----------
    x : ndarray
        Input array.  Must be positive 1-dimensional.  Must not be constant.
    lmbda : {None, scalar}, optional
        If `lmbda` is not None, do the transformation for that value.
        If `lmbda` is None, find the lambda that maximizes the log-likelihood
        function and return it as the second output argument.
    alpha : {None, float}, optional
        If ``alpha`` is not None, return the ``100 * (1-alpha)%`` confidence
        interval for `lmbda` as the third output argument.
        Must be between 0.0 and 1.0.
    optimizer : callable, optional
        If `lmbda` is None, `optimizer` is the scalar optimizer used to find
        the value of `lmbda` that minimizes the negative log-likelihood
        function. `optimizer` is a callable that accepts one argument:

        fun : callable
            The objective function, which evaluates the negative
            log-likelihood function at a provided value of `lmbda`

        and returns an object, such as an instance of
        `scipy.optimize.OptimizeResult`, which holds the optimal value of
        `lmbda` in an attribute `x`.

        See the example in `boxcox_normmax` or the documentation of
        `scipy.optimize.minimize_scalar` for more information.

        If `lmbda` is not None, `optimizer` is ignored.

    Returns
    -------
    boxcox : ndarray
        Box-Cox power transformed array.
    maxlog : float, optional
        If the `lmbda` parameter is None, the second returned argument is
        the lambda that maximizes the log-likelihood function.
    (min_ci, max_ci) : tuple of float, optional
        If `lmbda` parameter is None and ``alpha`` is not None, this returned
        tuple of floats represents the minimum and maximum confidence limits
        given ``alpha``.

    See Also
    --------
    probplot, boxcox_normplot, boxcox_normmax, boxcox_llf

    Notes
    -----
    The Box-Cox transform is given by::

        y = (x**lmbda - 1) / lmbda,  for lmbda != 0
            log(x),                  for lmbda = 0

    `boxcox` requires the input data to be positive.  Sometimes a Box-Cox
    transformation provides a shift parameter to achieve this; `boxcox` does
    not.  Such a shift parameter is equivalent to adding a positive constant to
    `x` before calling `boxcox`.

    The confidence limits returned when ``alpha`` is provided give the interval
    where:

    .. math::

        llf(\hat{\lambda}) - llf(\lambda) < \frac{1}{2}\chi^2(1 - \alpha, 1),

    with ``llf`` the log-likelihood function and :math:`\chi^2` the chi-squared
    function.

    References
    ----------
    G.E.P. Box and D.R. Cox, "An Analysis of Transformations", Journal of the
    Royal Statistical Society B, 26, 211-252 (1964).

    Examples
    --------
    >>> from scipy import stats
    >>> import matplotlib.pyplot as plt

    We generate some random variates from a non-normal distribution and make a
    probability plot for it, to show it is non-normal in the tails:

    >>> fig = plt.figure()
    >>> ax1 = fig.add_subplot(211)
    >>> x = stats.loggamma.rvs(5, size=500) + 5
    >>> prob = stats.probplot(x, dist=stats.norm, plot=ax1)
    >>> ax1.set_xlabel('')
    >>> ax1.set_title('Probplot against normal distribution')

    We now use `boxcox` to transform the data so it's closest to normal:

    >>> ax2 = fig.add_subplot(212)
    >>> xt, _ = stats.boxcox(x)
    >>> prob = stats.probplot(xt, dist=stats.norm, plot=ax2)
    >>> ax2.set_title('Probplot after Box-Cox transformation')

    >>> plt.show()